Micromachined rate and acceleration sensor and method

ABSTRACT

A monolithic substrate for acceleration and angular rate sensing. The substrate comprises a support frame, and a first accelerometer formed in the substrate. The first accelerometer has a proof mass including first and second opposite edges. A flexure connects the first edge of the proof mass to the support frame. The flexure defines a hinge axis for the proof mass. The first accelerometer further includes a pair of torsion stabilizing struts coupling a portion of the proof mass to the frame.

TECHNICAL FIELD

The invention relates to an apparatus and methods for determining theacceleration and rate of angular rotation of a moving body, and inparticular, one which is adapted to be formed, for example throughmicromachining, from a silicon substrate.

BACKGROUND OF THE INVENTION

The use of tactical grade inertia measuring units has been limited bytheir cost to high-priced systems such as military aircraft, missiles,and other special markets. The cost of inertia measuring units isdominated by the expensive discrete gyroscopes and discreteaccelerometers and attendant electronics used to drive and convert thesesignals for use in computer systems.

Other problems with inertial measuring units are high power consumptionand large package size. The problems of high power consumption and largepackage size further limit applications to larger equipment boxes inequipment racks. For example, a hockey puck sized tactical gradenavigator is not known in the prior art.

Still other problems with the prior art include a limitation in ratebias accuracy cause by modulation of the accelerometer due to couplingfrom the dither motion which causes phase angle sensitivity of the ratedata. A further limitation in rate bias accuracy is caused by modulationof the accelerometer due to coupling of external vibration componentscoupling into the rate data.

Exemplary rate and acceleration sensors, components of such sensors, andmethods of forming the same are described in the following patents allof which are assigned to the assignee of this disclosure, and all ofwhich are expressly incorporated herein by reference: U.S. Pat. Nos.5,005,413; 5,168,756; 5,319,976; 5,331,242; 5,331,854; 5,341,682;5,367,217; 5,456,110; 5,456,111; 5,557,046; and 5,627,314.

By way of background, the rate of rotation of a moving body about anaxis may be determined by mounting an accelerometer on a frame anddithering it, with the accelerometer's sensitive axis and the directionof motion of the frame both normal to the rate axis about which rotationis to be measured. For example, consider a set of orthogonal axes X, Y,and Z oriented with respect to the moving body. Periodic movement of theaccelerometer along the Y axis of the moving body with its sensitiveaxis aligned with the Z axis results in the accelerometer experiencing aCoriolis acceleration directed along the Z axis as the moving bodyrotates about the X axis. A Coriolis acceleration is that perpendicularacceleration developed while the body is moving in a straight line, dueto rotation of the frame on which it is mounted. The Coriolisacceleration acting on the accelerometer is proportional to the velocityof the moving sensor body along the Y axis and its angular rate ofrotation about the X axis. An output signal from accelerometer thusincludes a DC or slowly changing component or force signal Frepresenting the linear acceleration of the body along the Z axis, andperiodic component or rotational signal ω representing the Coriolisacceleration resulting from rotation of the body about the X axis.

The Coriolis component can be produced by vibrating the accelerometerand causing it to dither back and fourth along a line perpendicular tothe input axis of the accelerometer. If the frame on which theaccelerometer is mounted is rotating, the Coriolis accelerationcomponent of the accelerometer's output signal will be increasedproportional to the dither velocity. If the dither amplitude andfrequency are held constant, then the Coriolis acceleration isproportional to the rotation rate of the frame.

The linear acceleration component and the rotational componentrepresenting the Coriolis acceleration may be readily separated by usingtwo accelerometers adjacent to each other and processing their outputsignals using summed difference techniques. In U.S. Pat. No. 4,510,802,assigned to the assignee of the present invention, two accelerometersare mounted upon a parallelogram with their input axes pointing inopposite directions. An electromagnetic D'Arsonval coil is mounted onone side of the parallelogram structure and is energized with aperiodically varying current to vibrate the accelerometers back andforth in a direction substantially normal to their sensitive or inputaxes. The coil causes the parallelogram structure to vibrate, ditheringthe accelerometers back and forth. By taking the difference between thetwo accelerometer outputs, the linear components of acceleration aresummed. By taking the sum of the two outputs, the linear componentscancel and only the Coriolis or rotational components remain.

U.S. Pat. No. 4,510,801, commonly assigned to the assignee of thisinvention, describes a processing of the output signals of twoaccelerometers mounted for periodic, dithering motion to obtain therotational rate signal ω in the force or acceleration signal Frepresenting the change in velocity; i.e., acceleration, of the movingbody along the Z axis.

U.S. Pat. No. 4,510,802, commonly assigned to the assignee of thisinvention, describes a control pulse generator, which generates andapplies a sinusoidal signal of a frequency ω to the D'Arsonval coil tovibrate the parallelogram structure and thus the first and secondaccelerometer structures, with a dithering motion of the same frequencyω. The accelerometer output signals are applied to a processing circuit,which sums the accelerometer output signals to reinforce the linearcomponents indicative of acceleration. The linear components areintegrated over the time period T of the frequency corresponding to thedithering frequency to provide the force signal F, which represents thechange in velocity; i.e., acceleration, along the Z axis. Theaccelerometer output signals are also summed, whereby their linearcomponents cancel and their Coriolis components are reinforced toprovide a signal indicative of frame rotation. That different signal ismultiplied by a zero mean periodic function. The resulting signal isintegrated over a period T of the frequency ω by a sample and holdcircuit to provide the signal ω representing the rate of rotation of theframe.

The D'Arsonval coil is driven by a sinusoidal signal of the samefrequency ω which corresponded to the period T in which the linearacceleration and Coriolis component signals were integrated. Inparticular, the pulse generator applies a series of pulses at thefrequency ω to a sine wave generator, which produces the substantiallysinusoidal voltage signal to be applied to the D'Arsonval coil. A pairof pick-off coils produce a feedback signal indicative of the motionimparted to the accelerometers. That feedback signal is summed with theinput sinusoidal voltage by a summing junction whose output is appliedto a high gain amplifier. The output of that amplifier, in turn, isapplied to the D'Arsonval type drive coil. The torque output of theD'Arsonval coil interacts with the dynamics of the parallelogramstructure to produce the vibrating or dither motion. In accordance withwell known servo theory, the gain of the amplifier is set high so thatthe voltage applied to the summing junction and the feedback voltage areforced to be substantially equal and the motion of the mechanism willsubstantially follow the drive voltage applied to the summing junction.

U.S. Pat. No. 4,881,408 describes the use of vibrating beam forcetransducers in accelerometers. In U.S. Pat. No. 4,372,173, the forcetransducer takes the form of a double-ended tuning fork fabricated fromcrystalline quartz. The transducer comprises a pair of side-by-sidebeams which are connected to common mounting structures at their ends.Electrodes are deposited on the beams and a drive circuit applies aperiodic voltage signal to the electrodes, causing the beams to vibratetoward and away from one another, 180 degrees out of phase. In effect,the drive circuit and beams form an oscillator with the beams playingthe role of a frequency controlled crystal; i.e., the mechanicalresonance of the beams controls the oscillation frequency. The vibratingbeams are made of crystalline quartz, which has piezoelectricproperties. Application of periodic drive voltages to such beams causethem to vibrate toward and away from one another, 180 degrees out ofphase. When the beams are subjected to accelerating forces, thefrequency of the mechanical resonance of the beams changes, whichresults in a corresponding change in the frequency of the drive signal.When subjected to acceleration forces that cause the beams to be placedin tension, the resonance frequency of the beams and thus the frequencyof the drive signal increases. Conversely, if the beams are placed incompression by the acceleration forces, the resonance frequency of thebeams and the frequency of the drive signal is decreased.

U.S. application Ser. No. 07/316,399 describes accelerometers usingvibrating force transducers that require materials with low internaldamping to achieve high Q values that result in low drive power, lowself heating and insensitivity to electronic component variations.Transducer materials for high accuracy instruments also require extrememechanical stability over extended cycles at high stress levels.Crystalline silicon possesses high Q values, and with the advent oflow-cost, micro-machined mechanical structures fabricated fromcrystalline silicon, it is practical and desirable to create vibratingbeams from a silicon substrate. Commonly assigned U.S. Pat. No.4,912,990 describes a vibrating beam structure fabricated fromcrystalline silicon and includes an electric circuit for applying adrive signal or current along a current path that extends in a firstdirection along a first beam and in a second, opposite, direction alonga second beam parallel to the first. A magnetic field is generated thatintersect substantially perpendicularly to the conductive path, wherebythe first and second beams are caused to vibrate towards and away fromone another, 180 degrees out of phase.

Digital techniques employ stable, high frequency crystal clocks tomeasure a frequency change as an indication of acceleration forcesapplied to such vibrating beam accelerometers. To ensure preciseintegration or cosine demodulation, a crystal clock is used to preciselyset the frequency of the dither drive signal. The outputs from twoaccelerometers are fed into counters to be compared to a reference clocksignal produced by the crystal clock. A microprocessor reads thecounters and processes the data to provide a force signal F and arotational signal ω. The main advantage of digital processing is theability to demodulate with extreme precision. The short-term stabilityof the reference crystal clock allows the half cycle time basis to beprecisely equal. Thus, a constant input to the cosine demodulator ischopped up into equal, positive half cycle and negative half cyclevalues, whose sum is exactly zero.

In an illustrated embodiment, the two accelerometer signals are countedin their respective counters over a 100 Hz period (corresponding to ahundred Hz of the dither frequency ω and are sampled at a 400 Hz datarate corresponding to each quarter cycle of the dither motion. The twoaccumulated counts are subtracted to form the force signal F. Since thecounters act as an integrator, the acceleration signal is changeddirectly to a velocity signal. Taking the difference of the accelerationsignals tends to reject all Coriolis signals as does the counterintegration and locked period data sampling.

The Coriolis signals are detected by a cosine demodulation. The cosinedemodulated signals from the first and second accelerometers are summedto produce the Δθ signal. Again, the counters integrate the rate data toproduce an angle change. The sum also eliminates any linear accelerationand the demodulation cancels any bias source including bias operatingfrequency and accelerometer bias. The accelerometer temperature is usedin a polynomial model to provide compensation for all the coefficientsused to convert the frequency counts into output units. Thus, the scalefactor, bias and misalignment of the sensor axes are corrected over theentire temperature range.

The demodulation of the frequency sample is straightforward once thedata is gathered each quarter cycle. The cosine demodulation is simplythe difference between the appropriate half cycles. The linearacceleration is the sum of all samples.

SUMMARY OF THE INVENTION

The invention provides a monolithic substrate for acceleration andangular rate sensing. The substrate includes a support frame and anaccelerometer formed in the substrate. The accelerometer has a proofmass with first and second opposite edges. The accelerometer furtherincludes a flexure connecting the first edge of the proof to the supportframe. The flexure defines a hinge axis for the proof mass. Thesubstrate includes a first torsion stabilizing strut joined with andextending along a first strut length between the proof mass and thesupport frame. The first torsion stabilizing strut is positioned closerto the flexure than to the second edge. The first strut has a firstthickness dimension generally transverse the first strut length. Thesubstrate further includes a second torsion stabilizing strut joinedwith and extending along a second strut length between the proof massand the support frame. The second torsion stabilizing strut ispositioned closer to the flexure than to the second edge. The secondstrut has a second thickness dimension generally transverse the secondstrut length which is different in magnitude than the first thicknessdimension.

One aspect of the invention provides a monolithic substrate foracceleration and rate sensing. The substrate includes a support frameincluding a post, and an accelerometer formed in the substrate. Theaccelerometer has a proof mass including first and second legs and amain body portion connecting the legs and accommodating common movementof the legs. The accelerometer further includes a flexure includingfirst and second spaced apart flexure portions respectively connectingthe first and second legs to the support frame. The flexure defines ahinge axis for the proof mass. The post is disposed between the flexureportions and extends toward the main body portion and between the legs.The substrate includes a first torsion stabilizing strut joined with andextending along a first strut length between the proof mass and thepost. The first strut has a first thickness dimension generallytransverse the first strut length. The substrate further includes asecond torsion stabilizing strut joined with and extending along asecond strut length between the proof mass and the post. The secondstrut has a second thickness dimension generally transverse the secondstrut length which is different in magnitude than the first thicknessdimension.

Another aspect of the invention provides a monolithic substrate foracceleration and angular rate sensing. The substrate includes a supportframe and a first accelerometer formed in the substrate. The firstaccelerometer has a proof mass including first and second oppositeedges, and third and fourth opposite edges. A flexure connects the firstedge of the proof mass to the support frame and defines a hinge axis forthe proof mass. A first force-sensing member is coupled between theproof mass and the support frame. A first pair of torsion stabilizingstruts are joined with and extend between the proof mass and the supportframe along respective strut lengths. Individual struts of the pair arepositioned closer to the flexure than to the second edge and haverespective thickness dimensions generally transverse the respectivestrut lengths. A second accelerometer is formed in the substrate and hasa second proof mass including fifth and sixth opposite edges, andseventh and eighth opposite edges. A flexure connects the fifth edge tothe support frame and defines a hinge axis for the second proof mass. Asecond force-sensing member is coupled between the second proof mass andthe support frame. A second pair of torsion stabilizing struts arejoined with and extend between the second proof mass and the supportframe along respective strut lengths. Individual struts of the secondpair of struts are positioned closer to the flexure of the secondaccelerometer than to the sixth edge. The individual struts haverespective thickness dimensions generally transverse the respectivestrut lengths of the second pair of struts. In a preferred aspect, onepair of the first and second pairs of struts comprises an individualstrut having a thickness dimension which is different in magnitude fromthe other individual strut of the one pair.

The invention resolves significant problems of the prior art byproviding a small sized, low-cost, tactical grade navigator operableusing a computer to perform a variety of applications which heretoforecould not be addressed. For example, a tactical grade inertial measuringunit is too large, heavy and expensive to be carried by a guidedmunitions, a mini-air launch decoy, or a single person in a "dismountedsoldier" application.

The present invention provides a small sized, low-cost tactical gradenavigator having the following characteristics: a mass-produciblesensor; a small, easily fabricated inertial measuring unit; directdigital compatibility with a computer; and a simplified systemelectronics.

According to yet another aspect of the present invention, the presentinvention provides improved performance by providing two accelerometershaving matching natural frequencies and scale factors when the twoaccelerometers are manufactured simultaneously within a singlesubstrate.

According to yet another aspect of the present invention, the presentinvention provides reduced processing sensitivity by providing twoaccelerometers having matching natural frequencies and scale factorswhen the two accelerometers are manufactured simultaneously within asingle substrate.

According to still another aspect of the present invention, the presentinvention provides a reduced cost rate and acceleration sensor byproviding a simplified electrode pattern. According to yet anotheraspect of the present invention, the present invention provides reducedcost through simplified manufacturing by providing all electrode pathsformed on only one side of the substrate.

According to still another aspect of the present invention, the presentinvention provides simplified manufacturing and a simplified electronicsinterface by providing multiple hairspring flexures connecting thesensor to the input/output interconnects which permits all the electrodepaths to be formed on only one side of the substrate.

BRIEF DESCRIPTION OF THE DRAWINGS

Preferred embodiments of the invention are described below withreference to the following accompanying drawings.

FIG. 1 is a top plan view of a unitary substrate out of which are formeda pair of accelerometers in accordance with a preferred aspect of theinvention.

FIG. 2 is an enlarged, fragmentary view of a portion of one of the FIG.1 accelerometers, showing in particular, one force-sensing elementconfiguration.

FIG. 3 is an enlarged, fragmentary view of a portion of the other of theFIG. 1 accelerometers, showing in particular, one force-sensing elementconfiguration.

FIG. 4 is a view which is taken along line 4--4 in FIG. 2.

FIG. 5 is a view which is taken along line 5--5 in FIG. 2.

FIG. 6 is a view which is taken along line 6--6 in FIG. 2.

FIG. 7 is a view which is taken along line 7--7 in FIG. 2.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Copending U.S. application Ser. No. 08/786,185, filed Jan. 20, 1997,incorporated herein by reference, describes and claims an apparatus andmethod for determining the rate of angular rotation of a moving bodyand, in particular, one which is adapted to be formed throughmicromachining of a silicon substrate. Copending U.S. ProvisionalApplication No. 60,047,774, filed May 27, 1997, incorporated byreference herein, bearing attorney docket 491-97-008, entitled"Micromachined Rate and Acceleration Sensor," and listing as inventor Rand H. Hulsing, II, describes and claims an apparatus and methods forproviding an apparatus for acceleration and angular rate sensing.

A basic sensor configuration is described in U.S. Pat. No. 5,241,861,issued Sep. 7, 1993, and U.S. Pat. No. 5,331,853, issued Jul. 26, 1994,commonly assigned and incorporated herein by reference. The describedconfiguration includes two vibrating beam accelerometers fabricated in adither structure from a monolithic silicon wafer. One limiting factor inrate bias accuracy is the modulation of the accelerometer due tocoupling from the dither motion. This modulation can cause extreme phaseangle sensitivity of the rate data. Also, external vibration of thepackage can couple into the rate channel due to this phase anglesensitivity. The invented sensor and methodologies through which it canbe formed are directed to solving these and other problems.

FIG. 1 shows a monolithic substrate for acceleration and angular ratesensing generally at 10. The substrate includes a support frame 12including first and second posts 14, 16. The substrate further includesa first accelerometer 18 formed in the substrate. First accelerometer 18has a proof mass 20 including first and second opposite edges 22, 24respectively, and third and fourth opposite edges 26, 28 respectively.The proof mass includes first and second legs 30, 32 and a main bodyportion 34 connecting the legs and accommodating common movement of thelegs relative to frame 12 in response to an acceleration force. Firstaccelerometer 18 further includes a flexure 36 connecting first edge 22of proof mass 20 to support frame 12. Flexure 36 defines a hinge axisHA₁ for proof mass 20. Flexure 36 includes first and second spaced apartflexure portions 38, 40 respectively connecting the first and secondlegs 30, 32 to support frame 12. A portion of frame 12 which definesfirst post 14 extends intermediate first and second flexure portions 38,40 and toward the second edge 24. More particularly, first post 14 isdisposed between flexure portions 38, 40 and extends toward main bodyportion 34 and between legs 30, 32.

The substrate further includes a second accelerometer 42 formed in thesubstrate. Second accelerometer 42 is similar to the first accelerometer18. Second accelerometer 42 has a second proof mass 44 including fifthand sixth opposite edges 46, 48, and seventh and eighth opposite edges50, 52. Second proof mass 44 includes third and fourth legs 54, 56 and amain body portion 58 respectively connecting third and fourth legs 54,56 and accommodating common movement thereof. Second accelerometer 42further includes a flexure 60 connecting fifth edge 46 to support frame12. Second flexure 60 includes third and fourth spaced apart flexureportions 62, 64 respectively, connecting third and fourth legs 54, 56 tosupport frame 12. Second post 16 is disposed between third and fourthflexure portions 62, 64 and extends toward the main body portion 58 ofsecond accelerometer 42 between third and fourth legs 54, 56. Flexure 60defines a hinge axis HA₂ for second proof mass 44. Preferably, hingeaxis HA, and hinge axis HA₂ define a common axis. Hinge axis HA₂ iscloser to hinge axis HA₁ than it is to second edge 24 of proof mass 20.

A link 66 is provided and connects accelerometers 18, 42 together andacts as g rocker arm to ensure that the accelerometers can be dithered180° out of phase. A discussion of various aspects of the dynamics ofdithering as such pertains to accelerometers can be found in many of thereferences mentioned above. Link 66 includes three flexures 68, 70, and72 which operably connect the respective accelerometers. Flexure 70defines a rotation point for link 66 so that the link essentially actsas a rocker arm. Other links are described in more detail in U.S. Pat.No. 5,331,853, incorporated by reference above.

A plurality of contact pads T1, G1, R1, P1, D1, and D2, P2, R2, G2, andT2 are disposed along one side of substrate 10. These pads providecontacts through which desirable electrical connection can be made tooutsideworld circuitry for the dither drive, dither pick-off, beam ortine drives, and beam or tine pick-offs, some of which are discussed inmore detail below. Such contact pads are connected with pertinentconductive paths on frame 12 by virtue of a plurality of hair springconnectors or flexures which are discussed in more detail below.

FIG. 2 shows a portion of first accelerometer 18 in more detail. Thefirst accelerometer further includes a force-sensing assembly 74. In theillustrated and preferred embodiment, force-sensing assembly 74comprises a first force-sensing member which includes a first vibratableor vibrating beam 76 coupled to proof mass 20 at a location intermediatehinge axis HA₁ and second edge 24 (FIG. 1) with respect to a directionextending from first edge 22 to second edge 24. Beam 76 is also coupledto the proof mass intermediate third and fourth edges 26, 28 withrespect to a direction extending from third edge 26 to fourth edge 28.More particularly, first vibratable beam 76 includes an upper end 76awhich is coupled to proof mass 20 at a location intermediate hinge axisHA₁ and the main body portion 34 (FIG. 1) with respect to a directionextending from hinge axis HA₁ to main body portion 34. Beam 76 alsoincludes a lower end 76b which is coupled to frame 12 via post 14. Aconductive path 78 is operably coupled with first beam 76 and extends atleast partially along post 14.

First accelerometer 18 further includes as part of the illustrated forcesensing member, a second vibratable or vibrating beam 80 proximate firstbeam 76 and having an upper end 80a coupled to proof mass 20, and alower end 80b coupled to frame 12 via post 14. Beam 80 is coupled toframe 12 at a location intermediate hinge axis HA₁ and second edge 24(FIG. 1) with respect to a direction extending from first edge 22 tosecond edge 24. Beam 80 is also coupled intermediate third and fourthedges 26, 28 with respect to a direction extending from third edge 26 tofourth edge 28. More particularly, second vibratable beam 80 is coupledto post 14 at a location intermediate hinge axis HA₁ and main bodyportion 34 with respect to a direction extending from hinge axis HA₁ tomain body portion 34. A conductive path 82 is coupled to second beam 80and extends at least partially along post 14. In the illustratedembodiment, the entirety of beams 76, 80 of first accelerometer 18 aredisposed between hinge axis HA₁ of the first accelerometer and thesecond edge 24. The first and second beams are preferably elongatedalong respective directions that are both substantially normal to hingeaxis HA₁. The force-sensing member illustrated and discussed just above,is intended to present but one, non-limiting example of an exemplaryforce-sensing member which is suitable for use with the presentinvention. Accordingly, other force-sensing members, and ones which arenot necessarily vibratable in nature, could be employed.

The illustrated force-sensing assembly also includes a referenceresistor 84 in the form of beams 86, 88. Beams 86, 88 are tied togetherby a plurality of pins 90, 92, and 94. Beams 86, 88 do not vibrate andare provided to match the electrical path resistance of beams 76, 80. Aconductive path 96 is provided and operably connects with beams 86, 88.Each of conductive paths 78, 82, and 96 are connected via hair springflexures or connectors 78a, 82a, and 96a respectively, with electricalcontact pads (FIG. 1) which, in turn, make desirable electricalconnections with outside world circuitry. When an electrical current isprovided via the conductive path over vibrating beams 76, 80, a voltagedrop develops relative to those beams. Similarly, a current providedover beams 86, 88 develops a generally identical voltage drop such thatthe two voltage drops can be subtracted from one another and cancel.This assists outside circuitry in its discrimination of the feedbacksignals from the vibrating beams.

First accelerometer 18 further includes a pair of torsion stabilizingstruts which are joined with and extend between proof mass 20 and frame12. Exemplary first and second struts are shown respectively at 98, 99.For purposes of the ongoing discussion, the pair of torsion stabilizingstruts comprising struts 98, 99 provide a first pair of struts; and,strut 98 comprises "one" of the pair of individual struts and strut 99comprises the "other" of the pair of individual struts. Each respectivestrut extends along a strut length between the proof mass and the frame.Exemplary strut lengths for struts 98, 99 are respectively shown at L₁,L₂. Accordingly, strut length L₁ comprises a first strut length andstrut length L₂ comprises a second strut length. The struts haveindividual respective thickness dimensions generally transverse therespective strut lengths. An exemplary first thickness dimension forfirst strut 98 is shown at t₁, while an exemplary second thicknessdimension for second strut 99 is shown at t₂. In the illustratedexample, the first and second thickness dimensions are different inmagnitude from one another, with the first thickness dimension beingless in magnitude than the second thickness dimension. In one aspect,the magnitude of the first thickness dimension is between about 50% to90% of the magnitude of the second thickness dimension. Preferably, themagnitude of the first thickness dimension is between about 60% to 75%of the magnitude of the second thickness dimension. Even morepreferably, the magnitude of the first thickness dimension is about 70%of the magnitude of the second thickness dimension. Exemplary values forrespective thickness dimensions t₁ and t₂ are 25 microns and 35.4microns respectively.

FIG. 2 shows that first strut 98 includes a generally elongate portion98a and a somewhat shorter portion 98b. Portions 98a and 98b extendalong strut length L₁. Portion 98a joins with post 14 at one endproximate a joinder location and extends generally away therefrom alongstrut length L₁. In the illustrated example, that portion of strutlength L₁ corresponding to portion 98a is generally parallel with hingeaxis HA₁. Portion 98a joins up with portion 98b, with portion 98bextending generally away therefrom and toward edge 22 of proof mass 20where it joins therewith at a different joinder location. That portionof strut length L₁ which corresponds to portion 98b extends in adirection which is different from hinge axis HA₁.

FIG. 2 also shows that second strut 99 includes a generally elongateportion 99a and a somewhat shorter portion 99b. Portions 99a and 99bextend along strut length L₂. Portion 99a joins with post 14 at one endproximate a joinder location and extends generally away therefrom alongstrut length L₂. In the illustrated example, that portion of strutlength L₂ corresponding to portion 99a is generally parallel with hingeaxis HA₁. Portion 99a joins up with portion 99b, with portion 99bextending generally away therefrom and toward edge 22 of proof mass 20where it joins therewith at a different joinder location. That portionof strut length L₂ which corresponds to portion 99b extends in adirection which is different from hinge axis HA₁. In the illustratedexample, portions 98a and 99a extend generally away from one anotherfrom the respective joinder locations at which each joins with post 14.Portions 98b and 99b extend away from proof mass 20 from the respectivejoinder locations at which each joins with the proof mass and inrespective directions which are generally parallel with one another.

The struts also include portions which extend over flexure 36 andportions which extend over open areas intermediate flexures 36 and post14. In the illustrated example, and as viewed in FIG. 2, a little morethan one half of portions 98a, 99a extend over respective flexureportions 38, 40; and, a substantial part of portions 98b, 99b extendover respective flexure portions 38, 40. It will be understood that theabove-described strut construction and location is but one preferredexample, and that other constructions and locations are possible.Moreover, it is possible for the strut(s) to connect at locations otherthan those specifically shown and described. In the illustrated example,struts 98, 99 are positioned closer to flexure 36 than to second edge24.

FIGS. 4-6 show that proof mass 20 has first and second surfaces 100, 102defining respective first and second planes, and hinge axis HA₁ isgenerally parallel to such planes. Flexure 36 is closer to secondsurface 102 than to first surface 100 with respect to a direction normalto the first plane. At least a portion of struts 98, 99 respectivelyoverlie flexure 36. FIGS. 5 and 6 show respective portions of firststrut 98 which are oriented in respective planes which are generallytransverse the first strut length. First strut 98 has a first areadimension A₁ oriented in the illustrated planes. FIG. 7 shows a portionof second strut 99 which is oriented in a plane which is generallytransverse the second strut length. Second strut 99 has a second areadimension A₂ which is different from, and preferably greater than firstarea dimension A₁. In the illustrated example, the area differential isdue to a difference in the respective thickness dimensions t₁, t₂ withthe respective height dimensions h (FIGS. 6 and 7) of the struts beinggenerally equivalent. An exemplary height dimension is around 20microns.

FIG. 3 shows second accelerometer 42 in more detail. Secondaccelerometer 42 includes a force-sensing assembly 104. In theillustrated and preferred embodiment, force-sensing assembly 104comprises a second force-sensing member which includes a thirdvibratable beam 106 coupled to second proof mass 44 at a locationintermediate hinge axis HA₂ and sixth edge 48 (FIG. 1) with respect to adirection extending from fifth edge 46 to sixth edge 48. Beam 106 isalso coupled intermediate seventh and eighth edges 50, 52 with respectto a direction extending from seventh edge 50 to eighth edge 52.

Second accelerometer 42 further includes as part of the illustratedforce-sensing member, a fourth vibratable beam 108 proximate third beam106 and coupled to frame 12, i.e., post 16, at a location intermediatehinge axis HA₂ and sixth edge 48 (FIG. 1) with respect to a directionextending from fifth edge 46 to sixth edge 48. Beam 108 is also coupledintermediate seventh and eighth edges 50, 52 with respect to a directionextending from seventh edge 50 to eighth edge 52. In the illustratedembodiment, the entirety of beams 106, 108 are disposed between hingeaxis HA₂ of the second accelerometer and the sixth edge 48. Third andfourth beams 106, 108 are elongated along respective directions that areboth substantially normal to hinge axis HA₂ of the second accelerometer.The force-sensing member illustrated and discussed just above, isintended to present but one, non-limiting example of an exemplaryforce-sensing member which is suitable for use with the presentinvention. Accordingly, other force-sensing members, and ones which arenot necessarily vibratable in nature, could be employed.

The illustrated force-sensing assembly also includes a referenceresistor 110 in the form of beams 112, 114 which are tied together withthree pins 116, 118, and 120. Beams 112, 114 perform in substantiallythe same way as described above with respect to beams 86, 88 (FIG. 2) offirst accelerometer 18. Conductive paths are provided and by virtue ofthe dynamic operation of the accelerometers described just below, areconfigured somewhat differently than the electrical connections orconductive paths described above. Accordingly, a conductive path 122 isprovided and extends along post 16 to ultimately connect with and beformed over beam 106. A conductive path 124 is provided and extendsgenerally along a same path as conductive path 122 and connects withbeams 108 and 114. A conductive path 126 is provided and operablyconnects with beam 112. Each of conductive paths 122, 124, and 126 areconnected via hair spring connectors 122_(a), 124_(a), and 126_(a)respectively, with electrical contact pads (FIG. 1) which, in turn, makedesirable electrical connections with outside world circuitry.

Second accelerometer 42 further includes a pair of torsion stabilizingstruts which are joined with and extend between second proof mass 44 andframe 12. Exemplary first and second struts are shown respectively at128, 129. For purposes of the ongoing discussion, the pair of torsionstabilizing struts comprising struts 128, 129 provide a second pair ofstruts; and, strut 128 comprises "one" of the pair of individual strutsand strut 129 comprises the "other" of the pair of individual struts.Each respective strut extends along a strut length between the proofmass and the frame. Exemplary strut lengths for struts 128, 129 arerespectively shown at L₃, L₄. Accordingly, strut length L₃ comprises afirst strut length and strut length L₄ comprises a second strut length.The struts have individual respective thickness dimensions generallytransverse the respective strut lengths. An exemplary first thicknessdimension for first strut 128 is shown at t₃, while an exemplary secondthickness dimension for second strut 129 is shown at t₄. In theillustrated example, the first and second thickness dimensions aredifferent in magnitude from one another, with the first thicknessdimension being less in magnitude than the second thickness dimension.In one aspect, the magnitude of the first thickness dimension is betweenabout 50% to 90% of the magnitude of the second thickness dimension.Preferably, the magnitude of the first thickness dimension is betweenabout 50% to 65% of the magnitude of the second thickness dimension.Even more preferably, the magnitude of the first thickness dimension isabout 60% of the magnitude of the second thickness dimension. Exemplaryvalues for respective thickness dimensions t₃ and t₄ are 25 microns and40.5 microns respectively.

FIG. 3 shows that first strut 128 includes a generally elongate portion128a and a somewhat shorter portion 128b. Portions 128a and 128b extendalong strut length L₃. Portion 128a joins with post 16 at one endproximate a joinder location and extends generally away therefrom alongstrut length L₃. In the illustrated example, that portion of strutlength L₃ corresponding to portion 128a is generally parallel with hingeaxis HA₂. Portion 128a joins up with portion 128b, with portion 128bextending generally away therefrom and toward edge 46 of second proofmass 44 where it joins therewith at a different joinder location. Thatportion of strut length L₃ which corresponds to portion 128b extends ina direction which is different from hinge axis HA₂.

FIG. 3 also shows that second strut 129 includes a generally elongateportion 129a and a somewhat shorter portion 129b. Portions 129a and 129bextend along strut length L₄. Portion 129a joins with post 16 at one endproximate a joinder location and extends generally away therefrom alongstrut length L₄. In the illustrated example, that portion of strutlength L₄ corresponding to portion 129a is generally parallel with hingeaxis HA₂. Portion 129a joins up with portion 129b, with portion 129bextending generally away therefrom and toward edge 46 of proof mass 44where it joins therewith at a different joinder location. That portionof strut length L₄ which corresponds to portion 129b extends in adirection which is different from hinge axis HA₂. In the illustratedexample, portions 128a and 129a extend generally away from one anotherfrom the respective joinder locations at which each joins with post 16.Portions 128b and 129b extend away from proof mass 44 from therespective joinder locations at which each joins with the proof mass andin respective directions which are generally parallel with one another.

The struts also include portions which extend over flexure 60 andportions which extend over open areas intermediate flexures 60 and post16. In the illustrated example, and as viewed in FIG. 3, a little morethan one half of portions 128a, 129a extend over respective flexureportions 64, 62; and, a substantial part of portions 128b, 129b extendover respective flexure portions 64, 62. It will be understood that theabove-described strut construction and location is but one preferredexample, and that other constructions and locations are possible.Moreover, it is possible for the strut(s) to connect at locations otherthan those specifically shown and described. In the illustrated example,struts 128, 129 are positioned closer to flexure 60 than to sixth edge48. Additionally, the illustrated respective second or "other" struts99, 129 of first and second accelerometers 18, 42 are disposed closer toone another than the respective first or "one" struts 98, 128. It willbe understood that area dimensions of the first and second struts of thesecond accelerometer generally vary relative to one another, asdescribed above with respect to the first accelerometer. Of course, inthe preferred embodiment, the area dimensions of respective secondstruts 99, 129 are different because of the variance in the respectivethickness dimensions t₂, t₄.

FIGS. 2 and 3 show that portions of respective posts 14, 16 extend awayfrom frame 12 (FIG. 1) and into an area occupied by respective proofmasses 20, 44. Posts 14, 16, constitute portions of the frame. Theprovided posts enable desirable conductive paths, such as thosediscussed above, to be formed and established with the respectivevibrating beams mentioned above. For example, as viewed in FIG. 2, beams76, 80 have upper ends 76a, 80a respectively, which are connected toproof mass 20 proximate first leg 30. The beams also include lower ends76b, 80b respectively, which are connected to frame 12. FIG. 3 showsthat beams 106, 108 include upper ends 106a, 108a respectively, whichare connected to frame 12 via post 16. The beams also include respectivelower ends 106b, 108b which are connected to proof mass 44 proximatethird leg 54. By virtue of the above-described beam connections relativeto frame 12 and the respective proof masses configured thereon, when theproof masses experience an acceleration, both deflect in the samedirection. As a result, the vibrating beams on one proof mass are placedinto tension while the other vibrating beams are placed intocompression. By virtue of the change in the vibration frequency of therespective vibrating beams when either a tensive or compressive force isexperienced, acceleration can be ascertained via electrical circuitswhich are operably connected therewith and configured to determine suchdifferences.

The present invention resolves significant problems of the prior art byproviding a force-sensing member between the flexures. According to oneaspect of the present invention, the force-sensing member is located ina center region proximate the proof mass and comprises a pair ofvibratable beams. Improvements in rate bias accuracy are achieved bysubstantially eliminating the modulation of the accelerometer due tocoupling from the dither motion which can cause extreme phase anglesensitivity of the rate data. In another example, the present inventionsubstantially eliminates coupling of external vibrations into the ratechannel which was a limitation in the prior art due to phase anglesensitivity.

According to another aspect, performance is improved by substantiallyreducing induced modulation by providing each accelerometer with a pairof torsion stabilizing struts. In a preferred aspect, individual strutsof a pair have relative degrees of asymmetry. In the illustratedexamples, such asymmetry is present in the form of variable strutthickness dimensions.

Other advantages of locating the force sensing member according to thepresent invention include: that the preferred beams can be readilyrealized through micromachining techniques; the dither modulation can besubstantially eliminated or reduced to acceptably small levels; the twoaccelerometers can be made to match natural frequencies and scalefactors; and the structures can be fabricated with very low processingsensitivity.

Rate sensor accuracy is a function of full scale g-range, ditherfrequency and phase resolution. For the case of a sensor dithered at1400 Hz, an equivalent clock resolution of 10 nanoseconds and amisalignment of 70 μradians, the rate according to the present inventionexhibits a bias uncertainty on the order of 1 degree per hour. By usingthe illustrated center beam design, one aspect of which is describedabove, the accelerometer phase can be modeled to provide theabove-mentioned accuracy over the sensor's operational temperaturerange.

The above-described sensor is also easily fabricated and provides aconstruction which carries with it many convenient advantages. Forexample, the entire electrode path (beam connections, pick-off, anddither connections) are deposited on one side of the substrate. Previoussensors have required electrode paths on both sides of the substrate.This adds to processing complexity. Also, all of the sensor input/outputinterconnects are on one edge of the substrate. Locating theinput/output interconnects as such facilitates wire-bonding of the unitto the drive electronics. According to the present invention, theaddition of multiple hairspring flexures connecting each end of theaccelerometer block to the frame makes location of the input/outputinterconnects on one edge of the substrate possible. The multiplehairspring flexures add only a small percentage to the frequency of thedither, but allow all the paths needed to connect the dither drive,dither pick-off, tine drives and tine pick-offs. Thus, fabrication issimplified because electrodes are deposited on only one side of thesubstrate instead of on multiple parts.

The dither motion of the accelerometer induces a sinusoidal velocity onthe accelerometer which makes the accelerometer sensitive to rotationrate about an axis perpendicular to the motion. This motion can alsoinduce an unwanted motion of the proof mass out of plane which creates afrequency modulation of the force sensing member. This modulation makesit difficult to extract the modulation induced by rotation from themodulation induced by the excitation of this mode. Ideally, anaccelerometer would have no modulation induced by the motion at thedither frequency of the accelerometers. According to one embodiment ofthe present invention, the strut members are connected to an upperepitaxial surface and are suspended over the accelerometer flexures.This strut configuration provides dither modulation control whilereducing coupling into the accelerometer. The reduced coupling reducescoupling of external vibration and reduces bias errors. The presentinvention can be modelled to adjust undesirable modulation to within 1Hz of zero modulation by varying the symmetry, e.g. thickness dimension,of the individual struts as described above.

The above-described struts are preferably formed through siliconprocessing techniques which take into account the crystal structure ofthe silicon substrate and the etch characteristics along certain crystalplanes. Specifically, in FIGS. 4-6, exemplary strut 98 is defined inpart by an epitaxial shelf which is formed over the substrate. A surface130 is defined between first surface 100 and flexure 36. Surface 130defines a predetermined crystal plane. In the illustrated example,surface 130 defines the 111 crystal plane of the silicon substrate. AKOH etch is utilized, while the epitaxial shelf is back-biased, todesirably etch material from over flexure 36 and along surface 130. Thisetch desirably etches substrate material from underneath the epitaxialshelf defining strut 98. What is left after the etch is a cantileveredshelf which is disposed over flexure 36. Accordingly, the struts areformed. Formation of substrate 10 in general can take place throughmicromachining by various techniques such as wet and dry chemicaletching. For example, techniques such plasma etching, sputter etching orreactive ion etching (RIE) can be utilized. In a preferred aspect, RIEis utilized to micromachine the struts. For a detailed discussion ofsuch techniques, reference is made to the following publications, whichare incorporated herein by reference: VLSI Fabrication Principles bySorab K. Ghandhi, and Silicon Processing for the VLSI Era., Vols. 1-3,by S. Wolf & R. J. Tauber.

The push-pull beam or tine configuration uses the front side epitaxialsurface only which provides excellent pendulum natural frequencymatching. The tines each experience equal out-of-plane bending whichprovides good parameter matching. The invention provides separate driveand reference leads for the accelerometer tines. The dither drive andpick-off leads are separated and wrapped around to a common edge. Theinvention provides for small sensor size, on the order of 0.7-inch by0.5-inch which allows for up to 24 sensors per 4-inch silicon wafer.

The invention has been described in compliance with the applicablestatutes. Variations and modifications will be readily apparent to thoseof skill in the art. It is therefore to be understood that the inventionis not limited to the specific features shown and described, since thedisclosure comprises preferred forms of putting the invention intoeffect. The invention is, therefore, to be interpreted in light of theappended claims appropriately interpreted in accordance with thedoctrine of equivalents.

I claim:
 1. A monolithic substrate for acceleration and angular ratesensing, the substrate comprising:a support frame; an accelerometerformed in the substrate and having a proof mass with first and secondopposite edges; a flexure connecting the first edge of the proof mass tothe support frame; a first torsion stabilizing strut joined with andextending along a first strut length between the proof mass and thesupport frame and being positioned closer to the flexure than to thesecond edge, the first strut having a first thickness dimensiongenerally transverse the first strut length; and a second torsionstabilizing strut joined with and extending along a second strut lengthbetween the proof mass and the support frame and being positioned closerto the flexure than to the second edge, the second strut having a secondthickness dimension generally transverse the second strut length whichis different in magnitude than the first thickness dimension.
 2. Amonolithic substrate for acceleration and angular rate sensing inaccordance with claim 1, wherein the magnitude of the first thicknessdimension is between about 50% to 90% of the magnitude of the secondthickness dimension.
 3. A monolithic substrate for acceleration andangular rate sensing in accordance with claim 1, wherein the magnitudeof the first thickness dimension is between about 50% to 65% of themagnitude of the second thickness dimension.
 4. A monolithic substratefor acceleration and angular rate sensing in accordance with claim 1,wherein the magnitude of the first thickness dimension is between about60% to 75% of the magnitude of the second thickness dimension.
 5. Amonolithic substrate for acceleration and angular rate sensing inaccordance with claim 1, wherein the struts are joined with the supportframe proximate respective joinder locations and comprise respectiveportions proximate the respective joinder locations which extendgenerally away from one another.
 6. A monolithic substrate foracceleration and angular rate sensing in accordance with claim 1,wherein the struts are joined with the proof mass proximate respectivejoinder locations and comprise respective portions proximate therespective joinder locations which extend away from the proof mass ingenerally parallel directions.
 7. A monolithic substrate foracceleration and angular rate sensing in accordance with claim 1,wherein:the struts are joined with the support frame proximaterespective joinder locations and comprise respective portions proximatethe respective joinder locations which extend generally away from oneanother; and the struts are joined with the proof mass proximatedifferent respective joinder locations and comprise respective portionsproximate the different respective joinder locations which extend awayfrom the proof mass in generally parallel directions.
 8. A monolithicsubstrate for acceleration and angular rate sensing in accordance withclaim 1, wherein at least one of the first and second struts includes aportion which is disposed over the flexure.
 9. A monolithic substratefor acceleration and angular rate sensing in accordance with claim 1,wherein the first strut has a first area dimension oriented in a planegenerally transverse the first strut length, and the second strut has asecond area dimension oriented in a plane generally transverse thesecond strut length, the first strut area being different in magnitudethan the second strut area.
 10. A monolithic substrate for accelerationand angular rate sensing in accordance with claim 1, wherein each of thestruts includes a portion which is disposed over the flexure.
 11. Amonolithic substrate for acceleration and angular rate sensing inaccordance with claim 10, wherein the magnitude of the first thicknessdimension is between about 50% to 90% of the magnitude of the secondthickness dimension.
 12. A monolithic substrate for acceleration andangular rate sensing, the substrate comprising:a support frame includinga post; an accelerometer formed in the substrate and having a proof massincluding first and second legs and a main body portion connecting thelegs and accommodating common movement of the legs; a flexure includingfirst and second spaced apart flexure portions respectively connectingthe first and second legs to the support frame, the flexure defining ahinge axis for the proof mass, the post being disposed between theflexure portions and extending toward the main body portion and betweenthe legs; a first torsion stabilizing strut joined with and extendingalong a first strut length between the proof mass and the post, thefirst strut having a first thickness dimension generally transverse thefirst strut length; and a second torsion stabilizing strut joined withand extending along a second strut length between the proof mass and thepost, the second strut having a second thickness dimension generallytransverse the second strut length which is different in magnitude thanthe first thickness dimension.
 13. A monolithic substrate foracceleration and angular rate sensing in accordance with claim 12,wherein the magnitude of the first thickness dimension is between about50% to 90% of the magnitude of the second thickness dimension.
 14. Amonolithic substrate for acceleration and angular rate sensing inaccordance with claim 12, wherein the first strut includes at least aportion which is disposed over the first flexure portion, and the secondstrut includes at least a portion which is disposed over the secondflexure portion.
 15. A monolithic substrate for acceleration and angularrate sensing in accordance with claim 12, wherein the struts are joinedwith the post proximate respective joinder locations and at least one ofthe struts includes a portion proximate the respective joinder locationwhich extends generally away from the post in a direction which isgenerally parallel with the hinge axis.
 16. A monolithic substrate foracceleration and angular rate sensing in accordance with claim 12,wherein the struts are joined with the post proximate respective joinderlocations and both of the struts include portions proximate therespective joinder locations which extend generally away from the postin respective directions which are generally parallel with the hingeaxis.
 17. A monolithic substrate for acceleration and angular ratesensing in accordance with claim 12, wherein the struts are joined withthe proof mass proximate respective joinder locations and compriserespective portions proximate the respective joinder locations whichextend away from the proof mass in generally parallel directions.
 18. Amonolithic substrate for acceleration and angular rate sensing inaccordance with claim 17, wherein said parallel directions are differentfrom a direction defined by the hinge axis.
 19. A monolithic substratefor acceleration and angular rate sensing in accordance with claim 12,further comprising a force-sensing member coupled between the proof massand the post.
 20. A monolithic substrate for acceleration and angularrate sensing in accordance with claim 12, wherein:the struts are joinedwith the post proximate respective joinder locations and at least one ofthe struts includes a portion proximate the respective joinder locationwhich extends generally away from the post in a direction which isgenerally parallel with the hinge axis; and the struts are joined withthe proof mass proximate different respective joinder locations andcomprise different respective portions proximate the differentrespective joinder locations which extend away from the proof mass ingenerally parallel directions.
 21. A monolithic substrate foracceleration and angular rate sensing, the substrate comprising:asupport frame: a first accelerometer formed in the substrate, the firstaccelerometer having a proof mass including first and second oppositeedges, and third and fourth opposite edges, a flexure connecting thefirst edge of the proof mass to the support frame, the flexure defininga hinge axis for the proof mass, a first force-sensing member coupledbetween the proof mass and the support frame, and a first pair oftorsion stabilizing struts joined with and extending between the proofmass and the support frame along respective strut lengths, individualstruts of the pair being positioned closer to the flexure than to thesecond edge and having respective thickness dimensions generallytransverse the respective strut lengths; and a second accelerometerformed in the substrate, the second accelerometer having a second proofmass including fifth and sixth opposite edges, and seventh and eighthopposite edges, a flexure connecting the fifth edge to the supportframe, the flexure of the second accelerometer defining a hinge axis forthe second proof mass, a second force-sensing member coupled between thesecond proof mass and the support frame, and a second pair of torsionstabilizing struts joined with and extending between the second proofmass and the support frame along respective strut lengths, individualstruts of the second pair of struts being positioned closer to theflexure of the second accelerometer than to the sixth edge and havingrespective thickness dimensions generally transverse the respectivestrut lengths of the second pair of struts; at least one of the firstand second pairs of struts comprises a first strut having a thicknessdimension which is different in magnitude from a second strut of atleast one of the first and second pairs of struts.
 22. A monolithicsubstrate for acceleration and angular rate sensing in accordance withclaim 21 wherein the first and second pairs of struts each comprise anindividual strut having a thickness dimension which is different inmagnitude from the other individual strut of that pair of struts.
 23. Amonolithic substrate for acceleration and angular rate sensing inaccordance with claim 22 wherein:the magnitude of the thicknessdimension of one of the struts of the first pair of struts is betweenabout 50% to 90% of the magnitude of the thickness dimension of theother of the struts of the first pair of struts; and the magnitude ofthe thickness dimension of one of the struts of the second pair ofstruts is between about 50% to 90% of the magnitude of the thicknessdimension of the other of the struts of the second pair of struts.
 24. Amonolithic substrate for acceleration and angular rate sensing inaccordance with claim 23, wherein the other struts of the first andsecond pair of struts are disposed closer to one another than the onestruts of the first and second pair of struts.
 25. A monolithicsubstrate for acceleration and angular rate sensing in accordance withclaim 22 wherein:the magnitude of the thickness dimension of one of thestruts of the first pair of struts is between about 60% to 75% of themagnitude of the thickness dimension of the other of the struts of thefirst pair of struts; and the magnitude of the thickness dimension ofone of the struts of the second pair of struts is between about 50% to65% of the magnitude of the thickness dimension of the other of thestruts of the second pair of struts.
 26. A monolithic substrate foracceleration and angular rate sensing in accordance with claim 21wherein:the proof mass of the first accelerometer includes first andsecond legs between the third and fourth edges thereof, and a main bodyportion connecting the legs and accommodating common movement of thelegs; the proof mass of the second accelerometer includes third andfourth legs between the seventh and eighth edges thereof, and a mainbody portion connecting the legs of the second accelerometer andaccommodating common movement thereof; the flexure of the firstaccelerometer comprises first and second spaced apart flexure portionsrespectively connecting the first and second legs to the support frame;the flexure of the second accelerometer comprises third and fourthspaced apart flexure portions respectively connecting the third andfourth legs to the support frame; the support frame includes a first andsecond post, the first post being disposed between the first and secondflexure portions and extending toward the main body portion of the firstaccelerometer and between the first and second legs, the second postbeing disposed between the third and fourth flexure portions andextending toward the main body portion of the second accelerometer andbetween the third and fourth legs; individual struts of the first pairof struts being joined with the first post; and individual struts of thesecond pair of struts being joined with the second post.
 27. Amonolithic substrate for acceleration and angular rare sensing inaccordance with claim 26, wherein the first and second pairs of strutseach comprise a first strut having a thickness dimension which isdifferent in magnitude from a second strut of that pair of struts.
 28. Amonolithic substrate for acceleration and angular rate sensing inaccordance with claim 27, wherein:the magnitude of the thicknessdimension of one of the struts of the first pair of struts is betweenabout 50% to 90% of the magnitude of the thickness dimension of theother of the struts of the first pair of struts; and the magnitude ofthe thickness dimension of one of the struts of the second pair ofstruts is between about 50% to 90% of the magnitude of the thicknessdimension of the other of the struts of the second pair of struts.
 29. Amonolithic substrate for acceleration and angular rate sensing inaccordance with claim 26, wherein individual struts of the first pair ofstruts are joined with the first post proximate respective joinderlocations and both of the struts include portions which extend generallyaway from the first post in respective directions which are generallyparallel with the hinge axis of the first accelerometer.
 30. Amonolithic substrate for acceleration and angular rate sensing inaccordance with claim 26, wherein individual struts of the second pairof struts are joined with the second post proximate respective joinderlocations and both of the struts include portions which extend generallyaway from the second post in respective directions which are generallyparallel with the hinge axis of the second accelerometer.
 31. Amonolithic substrate for acceleration and angular rate sensing inaccordance with claim 26, wherein;individual struts of the first pair ofstruts are joined with the first post proximate respective joinderlocations and both of the struts include portions which extend generallyaway from the first post in respective directions which are generallyparallel with the hinge axis of the first accelerometer; individualstruts of the second pair of struts are joined with the second postproximate respective joinder locations and both of the struts of thesecond pair of struts include portions which extend generally away fromthe second post in respective directions which are generally parallelwith the hinge axis of the second accelerometer; the first and secondpairs of struts each comprise a first strut having a thickness dimensionwhich is different in magnitude from a second strut, the magnitude ofthe thickness dimension of the first strut of the first pair of strutsis between about 60% to 75% of the magnitude of the thickness dimensionof the second strute of the first pair of struts; and the magnitude ofthe thickness dimension of the first strut of the second pair of strutsis between about 50% to 65% of the magnitude of the thickness dimensionof the second strut of the second pair of struts.
 32. A monolithicsubstrate for acceleration and angular rate sensing in accordance withclaim 31, wherein said second struts of the first and second pair ofstruts are disposed closer to one another than said first struts of thefirst and second pair of struts.
 33. A method of forming a monolithicsubstrate for acceleration and angular rate sensing comprising:providinga substrate; forming a support frame within the substrate; forming anaccelerometer within the substrate, the accelerometer having a proofmass with first and second opposite edges; forming a flexure connectingthe first edge of the proof mass to the support frame; forming a firsttorsion stabilizing strut joined with and extending along a first strutlength between the proof mass and the support frame and being positionedcloser to the flexure than to the second edge, the first strut having afirst thickness dimension generally transverse the first strut length;and forming a second torsion stabilizing strut joined with and extendingalong a second strut length between the proof mass and the support frameand being positioned closer to the flexure than to the second edge, thesecond strut having a second thickness dimension generally transversethe second strut length which is different in magnitude than the firstthickness dimension.
 34. A method of forming a monolithic substrate foracceleration and angular rate sensing in accordance with claim 33,wherein the forming of the first strut comprises forming said strut tohave a first thickness dimension between about 50% to 90% of themagnitude of the second thickness dimension.
 35. A method of forming amonolithic substrate for acceleration and angular rate sensing inaccordance with claim 33, wherein the forming of the first strutcomprises forming said strut to have a first thickness dimension betweenabout 50% to 65% of the magnitude of the second thickness dimension. 36.A method of forming a monolithic substrate for acceleration and angularrate sensing in accordance with claim 33, wherein the forming of thefirst strut comprises forming said strut to have a first thicknessdimension between about 60% to 75% of the magnitude of the secondthickness dimension.
 37. A method of forming a monolithic substrate foracceleration and angular rate sensing in accordance with claim 33,wherein forming of the first and second torsion stabilizing strutscompirises reactive ion etching said struts from an epitaxial material.38. A method of forming a monolithic substrate for acceleration andangular rate sensing comprising:providing a substrate; forming a supportframe within the substrate; forming a first accelerometer within thesubstrate, the first accelerometer having a proof mass including firstand second opposite edges, and third and fourth opposite edges; forminga flexure connecting the first edge of the proof mass to the supportframe, the flexure defining a hinge axis for the proof mass; forming afirst force-sensing member coupled between the proof mass and thesupport frame; forming a first pair of torsion stabilizing struts joinedwith and extending between the proof mass and the support frame alongrespective strut lengths, individual struts of the pair being positionedcloser to the flexure than to the second edge and having respectivethickness dimensions generally transverse the respective strut lengths;forming a second accelerometer within the substrate, the secondaccelerometer having a second proof mass including fifth and sixthopposite edges, and seventh and eighth opposite edges; forming a flexureconnecting the fifth edge to the support frame, the flexure of thesecond accelerometer defining a hinge axis for the second proof mass;forming a second force-sensing member coupled between the second proofmass and the support frame; and forming a second pair of torsionstabilizing struts joined with and extending between the second proofmass and the support frame along respective strut lengths, individualstruts of the second pair of struts being positioned closer to theflexure of the second accelerometer than to the sixth edge and havingrespective thickness dimensions generally transverse the respectivestrut lengths of the second pair of struts, one pair of the first andsecond pairs of struts comprises a first strut having a thicknessdimension which is different in magnitude from a second strut of atleast one of the first and second pairs of struts.
 39. A method offorming a monolithic substrate for acceleration and angular rate sensingin accordance with claim 38, wherein the forming of the first and secondpairs of struts comprises forming each pair to have a first strut havinga thickness dimension which is different in magnitude from a secondstrut of that pair of struts.
 40. A method of forming a monolithicsubstrate for acceleration and angular rate sensing in accordance withclaim 39, wherein:the magnitude of the thickness dimension of one of thestruts of the first pair of struts is between about 50% to 90% of themagnitude of the thickness dimension of the other of the struts of thefirst pair of struts; and the magnitude of the thickness dimension ofone of the struts of the second pair of struts is between about 50% to90% of the magnitude of the thickness dimension of the other of thestruts of the second pair of struts.
 41. A method of forming amonolithic substrate for acceleration and angular rate sensing inaccordance with claim 40, wherein the forming of the first and secondpairs of struts comprises forming the second strut of the first pair ofstruts adjacent to the second strut of the second part of struts.
 42. Amethod of forming a monolithic substrate for acceleration and angularrate sensing in accordance with claim 38, wherein the forming of thefirst and second pairs of struts comprises reactive ion etching saidstruts from epitaxial material.